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Chapter 7: Problem 3

Why are there many more lines observed in the emission spectra of hydrogen and other elements than are found in their absorption spectra?

Short Answer

Expert verified
Emission spectra have more lines due to multiple downward transitions, while absorption involves fewer upward transitions.

Step by step solution

01

Understand Emission vs Absorption

Understand that emission spectra are produced when atoms release energy as photons after being excited, resulting in multiple possible transitions (from higher to lower energy levels). In contrast, absorption spectra are created when atoms absorb photons, promoting electrons to higher energy levels.
02

Consider Energy Level Transitions

Realize that in emission spectra, electrons can drop from any higher energy level to any lower energy level, leading to a wide range of transitions and thus a rich spectrum with many lines. Absorption involves transitions from a lower energy level (usually the ground state) to a higher state, resulting in fewer possible transitions and hence fewer lines.
03

Analyze Element Complexity

Note that in more complex elements, the number of possible transitions increases even further due to more complex energy level structures, contributing to the dense array of lines in emission spectra as opposed to the more limited spectrum of absorption.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Level Transitions
Energy level transitions are fundamental to understanding atomic spectra. Atoms have distinct energy levels where electrons can reside. These levels are quantized, meaning only specific energy levels are allowed. When an electron transitions between these levels, energy is either absorbed or emitted, depending on the direction of the transition.
  • Energy is absorbed when an electron moves from a lower energy level to a higher one. This forms the basis of absorption spectra.
  • Energy is emitted in the form of photons when an electron drops from a higher energy level to a lower one, leading to emission spectra.
In emission spectra, a multitude of transitions are possible. Electrons can descend to any lower level from a higher one, creating numerous spectral lines. In contrast, absorption spectra often involve an electron making a jump from the ground state to an excited state, limiting the number of observed lines.
Photon Emission
Photon emission is a key process in creating emission spectra. When an electron in an atom drops from a higher energy level to a lower one, it releases energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels.
  • The more levels an electron can transition between, the greater the variety of emitted photons.
  • This results in a rich, full spectrum with multiple spectral lines, especially in more complex atoms.
The energy of the photon determines its wavelength and thus its position in the electromagnetic spectrum. Different elements have their own unique sets of energy levels, leading to unique emission spectra. Photon emissions facilitate the identification of elements through spectroscopy.
Electronic Excitation
Electronic excitation occurs when an electron absorbs energy and is promoted to a higher energy level. This phenomenon is crucial for the formation of absorption spectra.
  • In absorption, electrons absorb specific photons and move to higher, excited states.
  • These specific photons correspond to the energy gap between the initial and final energy levels.
Notably, because electronic excitation often involves the promotion from the ground state to a higher energy level, the number of possible transitions is limited compared to emission. Consequently, absorption spectra typically exhibit fewer lines than their emission counterparts. This difference is particularly evident in hydrogen and other simple atoms, where potential transitions from the ground state are restricted.

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Most popular questions from this chapter

Assign the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) to the highest energy electron in the ground state of a lithium atom.

What is the wavelength, in nanometers, of an electron that is moving at a velocity of \(2.9 \times 10^{5} \mathrm{~m} / \mathrm{s} ?\)

What assumptions did Bohr make in explaining the hydrogen atom spectrum?

Sketch an orbital contour that is expected for an electron that has \(n=3\) and \(\ell=2\).

In each part, a set of quantum numbers is given. If the set is an allowed combination of \(n, \ell, m_{b}\), and \(m_{s}\), give the subshell to which this wave function belongs \((1 s, 2 s, 2 p\), and so on). If the combination of quantum numbers is not allowed, state why. (a) \(n=1, \ell=1, m_{\ell}=0, m_{s}=-\frac{1}{2}\) (b) \(n=4, \ell=2, m_{\ell}=2, m_{s}=+\frac{1}{2}\) (c) \(n=2, \ell=0, m_{\ell}=0, m_{s}=+\frac{1}{2}\) (d) \(n=3, \ell=0, m_{\ell}=1, m_{s}=-\frac{1}{2}\) (e) \(n=3, \ell=2, m_{\ell}=0, m_{s}=+\frac{1}{2}\) (f) \(n=6, \ell=0, m_{\ell}=0, m_{s}=+\frac{1}{2}\)
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